Football: Sunderland relegated from Premier League after Bournemouth defeat
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"My feeling at the start of the season was it was going to be a hard graft," Moyes told BBC Radio.
"But ultimately today I feel for the supporters. They pay their hard-earned cash to come to the stadium and we have not given them enough this season," he said.
Middlesbrough, who play on Sunday at home to Manchester City, are in 19th place on 27 points while Swansea, who are at Manchester United on Sunday, are on 31 points and Hull are on 34.
The only other goal on a low-key Saturday, with none of the top seven teams playing, came at the Hawthorns where Jamie Vardy struck the winner for Leicester against West Brom in the 43rd minute.
Vardy finished with confidence after Shinji Okazaki latched on to a poor back pass from Salomon Rondon.
Stoke City were held to a goalless draw at home to West Ham while Crystal Palace were hosting Burnley later on Saturday.
On Sunday, leaders Chelsea are away to Everton while second-placed Tottenham are at home to North London rivals Arsenal.

